29edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 212999628 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213002142 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-22 19: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-22 19:14:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213002142</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=<span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span>= | |||
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. | 29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents. | ||
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The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. | The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the [[The Archipelago|barbados triad]] 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. | ||
=Intervals= | |||
|| Degrees of 29-EDO || Cents value || | || Degrees of 29-EDO || Cents value || | ||
|| 0 || 0 || | || 0 || 0 || | ||
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|| 26 || 1075.862 || | || 26 || 1075.862 || | ||
|| 27 || 1117.241 || | || 27 || 1117.241 || | ||
|| 28 || 1158.621 ||</pre></div> | || 28 || 1158.621 || | ||
=Music= | |||
[[http://tinyurl.com/45lancy|Paint in the Water 29]] by [[Igliashon Jones]]</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>29edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>29edo</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
<!-- ws:end:WikiTextTocRule:10 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-size: 103%;">29 tone equal temperament</span></h1> | |||
<br /> | <br /> | ||
29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | 29edo divides the 2:1 octave into 29 equal steps of approximately 41.37931 cents.<br /> | ||
| Line 54: | Line 61: | ||
The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing.<br /> | The 3 is the only harmonic, of the intelligibly low ones anyway, that 29-edo approximates, and it does so quite well. Hence one possible use for 29edo is as an equally tempered pythagorean scale. However, it represents the 2.3.11/5.13/5 subgroup to very high accuracy, and 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the 1-11/7-13/7 chord, the <a class="wiki_link" href="/The%20Archipelago">barbados triad</a> 1-13/10-3/2, the minor barbados triad 1-15/13-3/2, the 1-14/11-3/2 triad and the 1-13/11-3/2 triad. 29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h1> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
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</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1> | |||
<a class="wiki_link_ext" href="http://tinyurl.com/45lancy" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a></body></html></pre></div> | |||